But the blue-eyed, rambunctious little girl has exceeded doctors' expectations.

"The majority of the progress I've seen in her, physically, mentally and emotionally" is due to cannabis, Barnhart told CNBC.

Moriah is one of four mothers who refer to themselves as the Cannamoms, advocating for medical marijuana to be legalized in all states so that their critically ill children, and others like them, can have access to a drug that is still illegal on the federal level.

Throughout her chemotherapy and beyond, Moriah said cannabis had helped Dahlia tremendously, but she can't get access to marijuana legally in Florida, where she lives.

Moriah and three other mothers made the journey from Florida to California to try cannabis for a protracted stay. All four at some point have given their children marijuana, and they say they witnessed an improvement in their well being afterward.

A few organizations, such as MedMen, the nonprofit Cann-I-Dream, and the medical marijuana dispensary Harborside Health Center, helped fund their visits and doctors' appointments of the parents who spoke to CNBC.

Dina Gusovsky | CNBC

A self-proclaimed "Cannamom" shows some of the medical cannabis she procured for her child.

They're not alone. The Cannamoms are part of just a handful of the hundreds of families from across the country who have relocated or are considering moving to a state where medical marijuana is legal.

"What we need to focus on is the unlawful laws that make us relocate or move to states that already have cannabis legally for medicinal purposes," Cannamom Renee Petro, whose son Branden suffers from intractable seizures, told CNBC.

Since the visit in mid-October, at least two of the mothers have decided to move to California.

Steve DeAngelo, co-founder of Harborside Health Center, argued that families should not have to uproot their lives in order to get access to cannabis.

"There's a lot of ways that a legal cannabis industry can bring financial and fiscal benefits to communities," DeAngelo told CNBC. "I hope that one of them isn't the continued migration of patients and parents from other states to California. I think that that's really a terrible way to build an industry."

Medical marijuana has brought in billions of dollars to states that have legalized it, and those numbers are likely to increase in the years to come if and when more states legalize.

But medical cannabis is not cheap. A regular consultation with California-based cannabis expert and family physician Dr. Frank Lucido costs up to $600 including a few follow-ups.

But not everyone agrees that marijuana should be considered as an option to treat some illnesses, especially in children.

"The negative side effects are basically anxiety, paranoia, potential psychosis, memory impairment, visual coordination impairment," Child and Adolescent Psychiatrist Dr. Ankur Desai told CNBC. "You have to think about the benefits and the risks. And at this point, it's about the benefits outweighing the risks, and I don't think we are there yet in terms of the empirical research and support."

On top of the emotional and physical stress these families have had to endure, the financial strains that come with finding the right marijuana can be difficult, as well.

One of the Cannamoms, Jacel Delgadillo, said she's spending tens of thousands of dollars to move from Florida to California and try to get her son, Bruno, who suffers from up to 400 seizures per day, some relief.

Anneliese Clark, whose daughter, Christina, has had three brain surgeries, told CNBC that the girl's claims that are covered by insurance are usually in the $250,000-to-$1 million range every year. But none of the cannabis claims are covered, she said.

Dr. Lucido cautioned against informing insurers or regular doctors about using cannabis, even in a state where it is legal, because of the potential negative consequences.

"In a perfect world, you should be able to tell your doctor everything," Lucido said. "But until insurance companies promise not to discriminate against people who use this safe and effective medicine there's a valid reason not to have cannabis mentioned in your regular medical records."